Thermal conductivity is a physical property of fundamental importance to the developers of highly insulating materials. Standard techniques for the direct steady-state measurement of thermal conductivity, greatly influenced by a long history of test development at national standards laboratories have been established. The majority of cases described in the literature for measuring low thermal conductivity specimens (on the order of the thermal conductivity of air) use specimen sizes varying from a few hundred centimeters to over a meter. However, researchers often develop advanced, highly insulating materials in small batches with specimen sizes too small for methods normally used to directly measure thermal conductivity. An example is the development of materials based on aerogels being performed at the National Aeronautics and Space Administration (NASA), Glenn Research Center. A need still exists for techniques to measure the thermal conductivity of small, low thermal conductivity materials.
Therefore, test samples may only be available in sizes too small for the methods normally used to directly measure thermal conductivity. Papers describing a National Institute of Standards and Technology (NIST)-sponsored test development effort from the late 1990s addressed this need, emphasizing materials used for building insulation. See, Flynn, D. R. and R. Gorthala, “Thermal Design of a Miniature Guarded Hot Plate Apparatus,” in Insulation Materials: Testing and Applications, ASTM STP 1320, R. R. Zarr and R. S. Graves, Editor, American Society for Testing and Materials, West Conshohocken, Pa., 1997, pp. 337-354. Also see, Michels, A. and A. Boltzen, “A Method for the Determination of the Thermal Conductivity of Gases at High Pressures” Physics, Vol. 18(8-9), 1952, pp. 605-612.
If the heat flow through an insulator were one dimensional, its thermal conductivity could be determined by measuring the electrical power required to attain a temperature gradient across a thin specimen of known thickness placed between two plates—one heated and one cooled. In practice, this assumption is seldom valid, particularly for very low conductivity specimens surrounded by insulation of comparable thermal conductivity.
Techniques for precisely measuring steady-state thermal conductivity are much more complex than they may initially appear. In principle, the thermal conductivity of an insulator can be measured by placing a thin sample of an unknown material between two plates—one heated and the other cooled—and measuring the electrical power required to attain a temperature gradient across a sample of known thickness. However, all the power coming from the heater does not automatically go into the sample, and the sample does not necessarily experience one-dimensional heat flow with parallel heat flux vectors through it. This is especially true for very low conductivity samples, where insulation around the edge of the sample could have thermal conductivity comparable to that of the sample.
Early in the 20th century, studies showed that one-dimensional heat flow could be approached by surrounding the disc and specimen assembly with temperature-controlled “guards” that minimized most of the heat flow in directions other than into the specimen. See, Dickinson, H. C. and M. S. V. Dusen, The Testing of Thermal Insulators. American Society of Refrigerating Engineers Journal, ASRE J., Vol. 3(2), 1916, pp. 5-25. Even with considerable care, this “guarded hot plate” approach is still imperfect and requires theoretical, and often experimental, corrections for imperfections in design, especially for measurements on low thermal conductivity insulators.
Such a guarded-hot-plate technique is represented by ASTM C177-04 and ISO 8302:1991. These standards describe an absolute method where thermal conductivity may be directly obtained from measurement of electrical power, temperatures, and specimen dimensions.
The guarded hot plate technique employs a meter plate surrounded by a guard plate—both of which are electrically heated, set to the same temperature, and separated by a gap. In two-sided designs, matched specimen plates are placed on each side of the meter- and guard-plates. In the single-sided design, the specimen (sample) is only placed against one side of the meter- and guard-plates; insulation and another heated guard are used in place of the second specimen. In both types of designs, the size of the plates is 0.1 to 1 m diameter or square, with the smaller size more appropriate for isotropic specimens. A “similarly constructed” cooler plate is placed on the far side of the specimen (sample) or specimens (samples).
In a vertical orientation, the major axis of the stack of heater-, specimen-, and cooler-plates is oriented vertically, while the longer dimension of the individual plates is oriented horizontally. In a horizontal orientation, the major axis of the stack is horizontal, while the individual plates are oriented vertically. The heater- and cooler-plates are preferably constructed from a high thermal conductivity metal, with electrical heaters arranged to ensure nearly isothermal plates. Temperature sensors, such as fine thermocouples, are used to measure the plate temperatures, which may be taken as the temperatures on each side of the specimen, assuming essentially zero contact resistance between the specimen and the plates. The standards permit using compliant spacers between the specimen and the plates to minimize contact resistance or, if the specimen is compliant, a small amount of specimen compression. For compliant specimens that would crush under the load of the clamping force holding the stack together, spacers are allowed to prevent crushing. The standards call for heater and cooler plates with high emissivity obtained through surface treatment, thus ensuring radiative, as well as conductive, heat transfer. The standards also call for a cylindrical guard—with axial gradient preferably matching the gradient of the stack—surrounding the entire assembly, and note that hours or even days may be required for the entire apparatus to achieve thermal equilibrium.
The standards stress three major points. First, great care must be taken to mathematically correct for design imperfections, including the effect of the gap between the meter plate and the guard plate and “edge heat flows at the periphery of the specimen”. Second, no one design is appropriate for every situation; each design must be considered on a case-by-case basis. Finally, the standards are not intended to be restrictive; research into new approaches is encouraged.
The guarded hot plate technique can be used for measurements of highly insulating specimens, but requires relatively large specimen sizes. A standard not applicable to highly insulating samples, but to small specimens is ASTM E1225-04. This standard uses a reference material placed on one or both sides of the test specimen and employs heater and cooler discs with a cylindrical guard surrounding the entire assembly. This technique differs from the guarded hot plate technique in that this guard may have an axial gradient matching the axial gradient of the stack of plates or be nearly isothermal with a temperature equal to the mean temperatures of the test specimen. The space between the walls of this guard and the stack are filled with powdered insulation. This technique is intended for test specimens having a thermal conductivity no lower than 0.2 W/m-° C., which is much greater than the thermal conductivity of air (about 0.026 W/m-° C. at room temperature).
Flynn and Gorthala, presented a design for a small guarded hot plate apparatus, 0.01 to 0.03 m square, for measuring specimens primarily in the conductivity range of 0.02 to 0.05 W/m-° C. The meter and guard on the cold plate side were to have a heat flux meter. See, Flynn, D. R. and R. Gorthala, “Design of a Subminiature Guarded Hot Plate Apparatus”, in Thermal Conductivity 23, K. E. Wilkes, R. B. Dinwiddie. R. S, Graves, Technomic, Lancaster, Pa., 1996, pp 46-55; Flynn, D. R. and R. Gorthala, “Thermal Design of a Miniature Guarded Hot Plate Apparatus,” in Insulation Materials: Testing and Applications, ASTM STP 1320, R. R. Zarr and R. S. Graves, Editor, American Society for Testing and Materials, West Conshohocken, Pa., 1996, pp. 337-354. Ceramic material was considered for the hot and cold meter and guard plates because their heating approach required an electrical insulator. The surfaces of the plates were to have been treated so as to have high emittance or to match the emittance to the end use of the material being tested. Flynn and Gorthala favored a single-sided guarded hot plate approach, noting that a significant mathematical correction would be required, especially involving heat flow across the gap. Flynn and Gorthala also favored an absolute measurement approach, noted the general lack of calibration standards for highly insulating materials, and expressed skepticism for using air as a reference standard. The apparatus was to have been of direct value in characterizing experimental products only available in very small specimen sizes. No evidence was found in the literature to indicate that this device was constructed.
Finally, when considering the use of air as a standard reference material, reviewing the use of the guarded hot plate approach for measuring the thermal conductivity of a gas is instructive. See, Michels, A. and A. Boltzen, “A Method for the Determination of the Thermal Conductivity of Gases at High Pressures” Physica, Vol. 18(8-9), 1952, pp. 605-612; and, Michels, A., J. V. Sengers, and P. S. V. D. Gulik, “The Thermal Conductivity of Carbon Dioxide in the Critical Region. I. The Thermal Conductivity Apparatus Physica, Vol 28, 1962, pp. 1201-1215. Michels et al. described an apparatus, that used highly polished copper plates having a silica coating to prevent tarnishing.
According to Smith, air may be used as a thermal conductivity reference material if sufficient care is taken. See, Smith, D. R., Thermal Conductivity of Fibrous Glass Board by Guarded Hot Plates and Heat Flow Meters: An International Round-Robin, International Journal of Thermophysics, Vol. 18(6), 1997, pp. 1557-1573. After examining the large systematic error in air conductivity measured in a round-robin study using relatively large 0.025 m air gaps, Smith recommended a single-sided design having vertical stack orientation, heater disc on top to minimize convective heat transfer, and limited air-cavity thicknesses. Example air-cavity thicknesses of 0.003 to 0.009 m were given. Smith further recommended that the air cavity be formed using a poorly conducting ring, and that measurement be made using multiple air-cavity thicknesses thus allowing the contributions due to conductive and radiative heat transfer to be separated out according to a technique described by Jaouen and Klarsfeld. See, Jaouen, J. L. and S. Klarsfeld, “Heat Transfer Through a Still Air Layer,” in Thermal Insulation: Materials and Systems. ASTM STP 922, F. J. Powell and S. L. Matthews, Eds., American Society for Testing and Materials, Philadelphia, 1987, pp 283-294. Smith was reporting a round robin study of the thermal conductivity of air which failed for multiple reasons including a directive that the sample be 0.025 m thick. Smith promoted a future round robin stating that at page 1571 “[i]n particular, such important parameters as the mean temperature of measurement, the temperature difference, the measured thickness, the range of ambient temperature, the pressure and humidity permitted or established in the laboratory during the measurement, and the order in which data points are to be measured must all be carefully considered. Some conditions (general laboratory ambient) may of necessity have to be left to the participant to decide upon, while other, more critical conditions (such as specimen conditioning for measurement of density and thermal conductivity) may have to be specified as mandatory. Care must be taken in specifying in advance the ambient conditions for measurement of related parameters such as density and thickness.”